After nominations are made, if there is only one nomination, the question is put to the committee. Traditionally, that decision is taken by asking for all those who are for and opposed. That's usually done by a voice vote, as we would do most normal votes in committee.
If the committee wishes, you can proceed by a secret ballot, but it would take the unanimous consent of the committee, as there is no provision for that in the Standing Orders. There are provisions for a secret ballot in the event that you have more than one motion for the position of chair.
Currently, there are no motions, but at the moment, the clerk is prepared to take motions for the position of chair.